Islam's first battle (The Battle of Badr) against the pagans of Mecca was
fought and won by 313 Muslims. In Shi'ism, it is believed that Imam al-Mahdi (the ultimate savior of the believers) will appear when there are 313 true and sincere Shia followers in the world. [Daniyal]

The paper Light and Number: Ordering Principles in the World of an Autistic Child by Park and Youderian begins on page 313 in the Journal of Autism and Childhood Schizophrenia (1974). Note that the Park's child Elly was fascinated by the "order" of numbers, especially primes.

The Roman emperor Constantine made Christianity the official religion in A.D. 313. [Pitts]

There are 313 exclamation marks in the KJV Bible! The first one occurs at the end of Genesis 17:18. [Bennet]

313 is the 13th centered square number. Note that 313 left-truncates to 13, which is also a prime. [Post]

This palindromic prime yields another and two more primes,
if its digits are replaced by their squares, cubes and
fourth powers. [Silva]

A fingerprint of Divinity is seen in this number in that it is a compound of two mirror-image emirps, 31, the Hebrew alpha-numberic value of the name GOD [EL = 1+30], and 13, the prime in the Hebrew name of Jehovah [YHVH = 10+5+6+5 = 26 = 2*13], hence, 31/13 compounded = 313. [Pitts]